Lloyds Ship Vibration and Noise Guidance Notes

Ship Vibration and Noise

Guidance Notes July 2006 Revision 2.1

ABCD

Enquires should be addressed to: Peter Filcek Technical Manager Technical Investigations (TID) Marine Consultancy Services Lloyd’s Register EMEA 71 Fenchurch Street London EC4M 4BS United Kingdom Telephone: +(44)207 423 1765 Fax: +(44)207 423 1804 Email: [email protected] Lloyd's Register is a trading name of the Lloyd's Register Group of entities. Services are provided by members of the Lloyd's Register Group, for details see www.lr.org/entities. The Lloyd's Register Group assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Lloyd's Register Group entity for the provision of this information or advice and in that case any responsibility or liability is exclusively on the terms and conditions set out in that contract.

© Lloyd's Register, 2006. All rights reserved. Except as permitted under current legislation no part of this work may be photocopied, stored in a retrieval system, published, performed in public, adapted, broadcast, transmitted, recorded or reproduced in any form or by any means, without prior permission of the copyright owner. Enquiries should be addressed to Lloyd's Register, 71 Fenchurch Street, London EC3M 4BS.

Ship Vibration and Noise Guidance Notes

CONTENTS

Contents July 2006

1

Revision 2.1 1

Section 1.

Introduction

3

1.1

Scope

3

1.2

Basis

3

1.3

Application of criteria

3

Section 2.

Measurement

4

2.1

Vibration

4

2.2

Noise

6

2.3

Hull surface pressures

10

Analysis

12

3.1

Vibration

12

3.2

Analysis for ISO 6954:1984

16

3.3

Analysis for ISO 6954:2000

18

3.4

Noise

20

3.5

Hull surface pressure data

22

Section 3.

Section 4.

Ship structure vibration

23

4.1

Hull girder

23

4.2

Superstructure modes

24

4.3

Acceptable vibration levels

25

Local structural vibration

26

Section 5. 5.1

General

26

5.2

Scope

26

5.3

Assessment

26

5.4

Alternative techniques

26

Accommodation and workspace vibration

28

6.1

Scope

28

6.2

Measurements

28

6.3

Test conditions

28

6.4

ISO 6954:1984 and ISO 6965:2000

28

6.5

Lloyd’s Register’s assessment of accommodation and

Section 6.

workspaces based on ISO 6954:1984 6.6

29

Assessment accommodation and workspaces based on ISO 6954:2000

Lloyd’s Register

31

6.7

Other ship types, PCAC

31

6.8

Motion sickness

31

i

Ship Vibration and Noise Guidance Notes

CONTENTS

Section 7.

Machinery vibration

32

7.1

Introduction.

32

7.2

Rotating machines

32

7.3

Reciprocating machines

34

7.4

Diesel alternator sets

36

7.5

Turbochargers

36

7.6

Reciprocating compressors

37

7.7

Main propulsion gearboxes

37

7.8

Rolling element bearings

37

7.9

Pipework

37

7.10

Electrical control and instrumentation

39

7.11

Vortex shedding

39

Section 8.

Noise

40

8.1

Scope

40

8.2

Objectives

40

8.3

Test conditions

40

8.4

Measuring positions

40

8.5

Assessment

40

8.6

Equivalent continuous sound level, L

40

8.7

Other ship types, PCAC

41

8.8

Noise transmission between cabins

41

Section 9.

Audible alarms and public address systems

44

9.1

Audible alarm levels

44

9.2

Public address system levels

44

9.3

Speech intelligibility

44

9.4

Preferred Speech Interference Level

45

Section 10.

Hull Surface Pressures

46

10.1

Introduction

46

10.2

Hull surface pressure levels

46

Section 11.

ii

Aeq

Related Standards, references and bibliography

48

11.1

Vibration - international standards

48

11.2

Vibration – national standards

49

11.3

Noise – international standards

49

11.4

Noise – national standards

50

11.5

References and bibliography

50

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Ship Vibration and Noise Guidance Notes

Section 1. 1.1

Section 1

Introduction

Scope These Vibration and Noise Guidance Notes are produced to assist in two main areas of shipboard activities: • •

1.2

Routine measurement surveys Investigation of problems.

Basis These Guidance Notes have been compiled from Lloyd’s Register’s experience of measuring, interpreting and assessing shipboard vibration and noise. In addition to Lloyd’s Register’s own criteria, certain existing International or National standards have been used in assessment of vibration and noise measurements. The proposed assessment criteria embody the experience gained in the interpretation, adaptation and extrapolation of these Standards in relation to shipboard conditions. Reference has also been made to other published information where applicable. These references and other relevant standards are listed in Section 11.

1.3

Application of criteria

1.3.1

These Guidance Notes define the application of proposed criteria for assessing the severity of shipboard vibration and noise in the following areas: • • • • •

Accommodation and workspaces, with regard to habitability Local structural vibration, with regard to risk of cracking Machinery vibration, with regard to risk of damage or accelerated wear Noise, with regard to loss of hearing and ease of verbal communication Hull surface pressure, with regard to propeller induced excitation.

1.3.2

Differences between ISO 6954:1984 and ISO 6954:2000 Guidelines for the overall evaluation of vibration in merchant ships are covered.

1.3.3

These Guidance Notes do not cover torsional, axial, or lateral vibration of shafting systems.

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Ship Vibration and Noise Guidance Notes

SECTION 2

Section 2.

Measurement

2.1

Vibration

2.1.1

Units Vibration velocity amplitude (± mm/s) is adopted in these Guidance Notes as the principal parameter for evaluating shipboard vibration. Unless specified otherwise vibration amplitude, ± a, is half the peak to peak value of the vibration, Figure 2.1. Vibration can also be measured in displacement or acceleration. Displacement tends to emphasise the lower frequencies, whilst acceleration emphasises the higher frequencies. The relationship between the three parameters for a sinusoidal waveform is given in Figure 2.1. The preferred units of measurements are: • • •

displacement, ± mm velocity, ± mm/s acceleration, ± m/s2.

Acceleration is also commonly expressed as a ratio of the acceleration due to gravity, “g”, where 1 g = 9.81 m/s2. The abbreviation “Gal”, for Galileo, is sometimes encountered, where 1 Gal = 1 cm/s2 = 10-2 m/s2. Figure 2.1 Vibration relationships for sinusoids.

Root mean square (r.m.s.), average and peak values are related by:

2.1.2

peak, ± a

peak to peak = 2a

Time

r.m.s.

average

Amplitude

r.m.s. value =

crest factor =

π

2 2

.average value =

1 2

. peak value

peak r.m.s.

For a sinusoidal waveform: displacement,

y

=

a.sin(2πn.t)

velocity,

v

= =

dy/dt (2πn).a.cos(2πn.t)

acceleration,

f

= = =

dv/dt d2y/dt2 -(2πn)2.a.sin(2πn.t)

where

n t

= =

frequency, Hz time, seconds.

Peak and r.m.s. values Hull structure, habitability and reciprocating machinery criteria use the peak vibration amplitude. The root mean square (r.m.s.) value is related to the energy content and is used in measurements of rotating machinery vibration.

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Section 2

In habitability and comfort measurements to ISO 6954:2000 an overall weighted r.m.s. velocity is used. In this case a frequency dependant weighting function is applied to the measurement signal which is intended to modify the data in a way which represents the human perception of whole-body vibration at discrete frequencies in the range 1 to 80 Hz as detailed in ISO 2631-2. The units should be clearly identified. 2.1.3

Broadband and narrowband Vibration amplitudes are often measured using a simple digital or analogue meter giving a single value representing either the peak or r.m.s. amplitude across a range of frequencies (defined by the characteristics of the transducer and meter). This is known as the overall or broadband value. Conversely, a narrowband measurement is one which is limited to a small range of frequencies usually centred on a frequency of interest. The smallest width is determined by the resolution of the analyser.

2.1.4

Conversion of measurements It is not possible to convert from broadband r.m.s. to peak or vice-versa unless the individual frequencies and amplitudes (also phase angles for r.m.s. to peak) are known. In these cases a detailed narrowband analysis is required. The relationship between an overall r.m.s. value xoa.rms, the r.m.s. components x1.rms, x2.rms, x3.rms..., and the peak amplitudes x1.pk, x2.pk, x3.pk....., at frequencies 1, 2, 3,....., is as follows: 2 xoa.rms = x1.rms + x22.rms + x32.rms + K

⎛x = ⎜⎜ 1. pk ⎝ 2 =

2

⎞ ⎛ x2. pk ⎟⎟ + ⎜⎜ ⎠ ⎝ 2

(

2

⎞ ⎛ x3. pk ⎟⎟ + ⎜⎜ ⎠ ⎝ 2

2

⎞ ⎟⎟ + K ⎠

)

1 2 x1. pk + x22. pk + x32. pk + K 2

The measurement unit should be selected with care, especially when comparison is to be made against these Guidance Notes or international standards. 2.1.5

Crest factor The crest factor is a number relating the maximum amplitude of the waveform to the r.m.s. value. Shipboard vibration signals commonly have crest factors between 2 and 4 if the propeller is the predominant excitation. For a regular sinusoidal waveform the crest factor is 2 as defined in Figure 2.1.

2.1.6

Transducers and filters Measurements should be made with an electronic system employing transducers which generate signals proportional to velocity or acceleration. Integrators may be used for conversions of velocity signals to displacement, or acceleration signals to velocity or displacement.

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SECTION 2

Transducers should be mounted using permanent magnets, studs, hard glue or beeswax. Mounting surfaces should be clean and free of debris, paint, rust, etc. Handheld probes are not recommended for single measurement applications where good accuracy is required. They may however be used in certain monitoring applications where care is taken to ensure repeatability. Filters may be used to restrict the frequency range of broadband measurements. They should be used with care to avoid attenuation and phase change to signals. 2.1.7

Standards The specifications for vibration transducers, filter characteristics, signal conditioning, display and recording equipment and calibration procedures should conform to International standards as listed in Section 11.

2.1.8

Calibration The measuring system should be calibrated in all vibration units of interest before and after the measurements. The calibration should be traceable to national standards. The characteristics of the measuring system shall be known from calibration with regard to the following: • • •

2.1.9

frequency response effect of transducer orientation and cable length temperature and other environmental conditions.

Records Permanent records of vibration measurements may be in the form of: • • • •

Binary/ASCII computer files Analogue/digital magnetic tapes Plots of vibration spectra from a narrowband frequency analysis Thermal/ultra-violet oscillograph paper

2.2

Noise

2.2.1

Sound pressure level, Lp Sound pressure levels (SPL) are measured in decibels (dB) using a logarithmic scale where the sound level Lp is given by: L p = 20 log 10

p dB po

where p is the measured root mean square sound pressure level in Pascals and po is the reference sound pressure level, 20 x 10-6 Pa. Note: 1 Pascal = 1 N/m2. The relationship between dB and the pressure ratio p/po is given in Table 2.1. A subjective assessment of changes in sound pressure levels is given in Table 2.2. and typical sound pressure levels in dBA (see para. 2.2.3) are given in Table 2.3. 6

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Ship Vibration and Noise Guidance Notes

Section 2

Table 2.1 Conversion of dB and pressure ratio.

Table 2.2 Subjective changes in pressure levels.

Pressure Ratio

- dB +

Pressure Ratio

Pressure Ratio

- dB +

Pressure Ratio

1.000

0

1.000

0.0316

30

31.62

0.891

1

1.122

0.0100

40

100

0.708

3

1.413

0.0032

50

316.2

0.501

6

1.995

0.0010

60

1000

0.316

10

3.162

0.0001

80

104

0.100

20

10.000

10

100

105

-5

Table 2.3 Typical sound pressure levels. Sound level

Description

0 dBA

Quietest perceivable sound

20-30 dBA

Countryside at night, quiet bedroom

30-40 dBA

Whispered conversation

Change in level

Perceived effect

3 dBA

just noticeable

6 dBA

noticeable

10 dBA

twice as loud

Table 2.4 Octave band frequencies and A-weighting Octave band nominal centre frequency Hz

Lower passband frequency Hz

Upper passband frequency Hz

A-weighting correction

31.5

22

45

-39

45

89

-26

dB

40-50 dBA

Domestic living room

63

50-60 dBA

General office

125

89

178

-16

60-70 dBA

Face to face conversation

250

178

355

-9

70-80 dBA

Town centre traffic, domestic vacuum cleaner

500

355

708

-3

80-90 dBA

Train at 100 m., engine room flats

1,000

708

1,410

0

90-100 dBA

Heavy engineering works, near cylinder heads on slow speed diesel at full power

2,000

1,410

2,820

+1

4,000

2,820

5,620

+1

100-110 dBA

Near pneumatic drill, grinder

8,000

5,620

11,200

-1

125 dBA

Pain threshold

16,000

11,120

22,400

-7

2.2.2

Frequencies of interest The normal frequency range of hearing of young adults is approximately 20 to 18,000 Hz. The frequency range of human speech is principally between 350 and 3,500 Hz.

2.2.3

A-weighted sound pressure level, LpA. Sound pressure level measurements relating to effect of noise on humans should be made in decibels using an A-weighting filter, dBA. The A-weighted frequency filter is used to reproduce the frequency response of the human ear. The A-weighting corrections are given in Table 2.4.

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SECTION 2

2.2.4

Equivalent continuous sound level, L Aeq,T This is the notional A-weighted, continuous, steady sound pressure level that, within a specified time interval T, has the same mean square sound pressure level as a sound whose level varies with time. It is defined by:

⎡ 1 t2 p A 2 (t ) ⎤ = 10 log10 ⎢ ∫ 2 dt ⎥⎥ ⎢⎣ t 2 − t1 t1 p 0 ⎦

L Aeq ,T where:

t2 - t1 = time interval, T pA(t) = instantaneous A-weighted sound pressure level p0

= reference sound pressure level

For a continuous, unvarying noise, LAeq is numerically the same as LpA. It is therefore possible to use a conventional sound level meter to determine LAeq if the noise levels for the whole period vary by less than 5 dB with a slow meter response. 2.2.5

Measurement technique Measurements can be made using LAeq (or Leq as necessary) if the sound level meter has the capability. This is often easier and less subjective than using LpA or Lp. LAeq should be used whenever the LpA fluctuates by more than 5 dB, or the sound is cyclic, irregular, or intermittent. Readings should made to the nearest decibel. The microphone should be at head height, 1.21.6 metres above deck, and pointed towards the dominant noise source if any. Measurements should normally be taken in the middle of spaces and no closer than 1 metre from bulkheads and major reflecting sources. If measurements are made using LpA or Lp, the meter should be set to “slow” response except where noise levels approach the overriding limits. A measuring time of at least 5 seconds should be allowed. If the level fluctuates by no more than 5 dB, an average of the maximum and minimum excursions can be made by eye.

2.2.6

Octave band filters If the maximum noise level for a space is exceeded or if subjectively annoying tones are present, then the unweighted noise level in each of the octave bands should be determined. The levels in each band are used to determine the Noise Rating number, Section 3.4. The octave band frequencies cover the normal range of human hearing frequencies and are listed in Table 2.4. The bands have a ratio of upper to lower frequencies of 2 and are centred on preferred frequencies given in ISO 266. Octave bands are comparatively coarse and use is sometimes made of third-octave bands.

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2.2.7

Section 2

Equipment standards Sound level meters can be either precision or industrial grade. Meters should conform to international standards, for example IEC 651 type or better and IEC 804 type 2 or better for integrating-averaging meters. Precision meters have an accuracy of about ±1 dB; industrial grade meters have an accuracy of about ±3 dB. A factor of 3 dB should be added to industrial grade meter readings to cater for the reduced accuracy. The use of a precision grade meter is, therefore, recommended where the noise levels are likely to be close to the recommended levels or in cases of dispute. Octave filter sets should conform to IEC 225 or equivalent. Microphones should be of the random incidence type and should conform to IEC 179 and IEC 651 (Types 1 and 2) or equivalent.

2.2.8

Calibration A suitable calibrator, approved by the manufacturer of the particular sound level meter, should be used. Calibrators for precision meters should be accurate to ± 0.3 dB and for industrial meters to ± 0.5 dB. The sound level meter, octave filter set and calibrator should be returned to the manufacturer or other organisations which provide a calibration traceable to national standards at intervals not exceeding two years.

2.2.9

Wind screens A microphone windscreen should be used when taking readings on bridge wings, on open deck, or below decks where there is any substantial air movement.

2.2.10

Recordings A tape recorder having a linear response in the frequency range 20 to 20,000 Hz should be used in cases of dispute or investigation work.

2.2.11

Speech intelligibility Speech intelligibility over public address and similar systems may be determined using techniques such as the Speech Interference Level (SIL) or Rapid Speech Transmission Index (RASTI). See also Chapter 9.

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SECTION 2

2.3

Hull surface pressures

2.3.1

Pressure transducers

Ship Vibration and Noise Guidance Notes

The pressure transducers, signal conditioning, and recording system should have a frequency response range which will measure the impulsive pressures arising from cavitation. An upper frequency response of about 5,000 Hz should be adequate for most purposes. Corrosion resistant pressure transducers should be used. Ideally the sensitive membrane of the transducer should be flush with the outer hull surface in order to avoid unwanted pressure harmonics. The design of available transducers and fitting sometimes make this difficult to achieve in practice. 2.3.2

System calibration The pressure transducers and complete recording system should be calibrated before and after the measurements.

2.3.3

Pressure components The hull surface pressure comprises two components. The first is the direct radiated pressure from the propulsor and the second is a self induced pressure resulting from the vibration of the transducer mounted on the hull. To separate these two components it is necessary to measure the vibration at the pressure transducer locations. This data, via suitable transformation methods, can be used to estimate the self-induced pressure components in terms of amplitude and phase at the transducer location.

2.3.4

Measurement locations The number of pressure transducers should, ideally, be between five and seven. For a righthanded propeller of diameter D, four pressure transducers should be placed at 0.05D to starboard of the shaft centreline, Figure 2.2. The longitudinal positions should be in the measurement reference plane shown in Figure 2.2, at intervals of 0.15D, starting at 0.10D aft of the propeller tip plane. At the plane 0.05D ahead of the propeller tips additional transducers may ideally be placed at 0.10D to port and 0.15D and 0.25D to starboard. The mirror image of this pattern should be applied for a left handed propeller. For ships with significant areas of shell plating aft of the propeller plane, pressure transducers may also be required to be located at distances up to 2D aft of the propeller plane in line with the principal tip vortex activity in the wake peak.

2.3.5

Phase marker A phase marker or angular position indicator should be fitted to the inboard shafting. It is convenient if this coincides with a particular blade at a known angular position of the propeller.

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2.3.6

Section 2

Visual observation Consideration should also be given to fitting viewing ports in the hull to allow boroscopes or video cameras and stroboscopic lighting to be used for observation in cases where severe cavitation occurs.

Figure 2.2 Propeller pressure measurement positions.

Measurement reference plane 0.10D 0.05D 0.15D

0.15D

Mid-chord

0.8 Diameter

Port 0.10D Shaft centreline 0.05D 0.10D

Starboard

0.10D

Drawn for right-hand propeller, looking from above. Positions for left-hand propeller are reversed in mirror image about shaft centreline.

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Ship Vibration and Noise Guidance Notes

SECTION 3

Section 3.

Analysis

3.1

Vibration

3.1.1

Narrowband analysis Narrowband frequency analysis is the recommended method of interpreting vibration measurements in relation to the guidance limits or for investigation purposes. Narrowband frequency analysis should be capable of resolving the frequency of individual components of interest over the relevant frequency range.

3.1.2

Broadband limits Some guidance values based on broadband measurements of the overall amplitude of composite frequency vibration are suggested in later sections to simplify routine survey procedures. Broadband measurements should cover the specified range of vibration frequencies for each particular application. If the acceptability of vibration severity is marginal from the results of broadband measurements, narrow band frequency analysis should be used. Records of the vibration measurements should be taken in such cases.

3.1.3

Orders of vibration Vibration frequencies can conveniently be related to a known fundamental excitation frequency by the use of order numbers. In cases where shaft rotational frequency is an appropriate reference, then:

Order number =

Vibration frequency Shaft rotational frequency

Order numbers are typically integer numbers, 1, 2, 3,......,n. Vibration at four cycles per shaft revolution arising from a four-bladed propeller, for example, can either be described as occurring at shaft fourth order or at blade order. Half orders (½, 1½, ...) may typically occur with 4-stroke diesel engines where the working cycle takes place over two shaft revolutions. 3.1.4

Analysis methods Vibration data can be divided into two categories: steady and transient. Some data with minimal transient characteristics can be considered in a quasi-steady sense. The available analysis methods are summarized in Figure 3.1.

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Section 3

Figure 3.1 Summary of available analysis methods Steady signal

Non-steady signal

Time series

Fourier analysis (FFT)

Joint Time Frequency (JTFA)

Spectrograms (Linear JTFA)

Distributions (Bilinear JTFA)

Time scale

Wavelets

Cohen's Class

Power spectra

3.1.5

Short time Fourier transforms Wigner-Ville (STFT) Choi-Williams Gabor spectrograms Cone-shped Data Other dependent Adaptive spectrograms

Daubechies Haar Specific design

Fast Fourier Transform analysis Analysis of steady and quasi-steady signals is usually carried out using the Fast Fourier Transform (FFT) function found on most vibration analysers. An FFT analysis transforms consecutive samples (typically 1024, 2048, or 4096) from the time domain to the same number of lines in the frequency domain. The algorithm used to calculate the FFT is finite and discrete. This has a number of effects. The first is that aliasing might occur, when because of a limited number of samples, high frequencies might appear as false lower frequencies. This is avoided by lowpass “antialiasing” filters. A sampling frequency higher than the maximum frequency of interest, fmax , is used. This is determined by: f max =

sampling frequency 2

The frequency resolution is thus dependent on the frequency range used, but most analysers have band- selectable analysis which gives increased resolution or “zoom” at frequencies of interest. The second effect of a finite sample record is that discontinuities can arise at the ends of the sample, giving rise to false results when the signal is not periodic in the time record. This causes leakage of energy from one resolution line of the FFT into other lines. The amplitude at the start and end of each block of samples is therefore reduced to zero, a technique known as windowing. The Hanning window is a good, general purpose compromise for continuous signals. A transient signal, such as from an impact, is self-windowing and a Uniform (Rectangular) window should be used. The third effect is known as the picket fence effect. It arises from the discrete sampling of the spectrum in the frequency domain in which the FFT acts like a series of parallel filters. The results are similar to viewing the results through slits in a picket fence. The shape or response of the filters is determined by the window function used. The amplitude of a frequency which is in the middle of a filter using a Hanning window will be measured accurately. A frequency midway between filters could be attenuated by up to 1.5 dB (18%). The use of a Flat-top window will reduce the possible attenuation to less than 0.1 dB (1%). However, the increase in accuracy comes at the expense of frequency resolution of small components. Lloyd’s Register

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SECTION 3

Time domain signal It is desirable to view the “raw” vibration signal (signal amplitude displayed against time) during analysis. Signal characteristics such as beating, transients and irregularities can be readily detected in the time domain. Approximate inspection methods of analysis are recommended as a check on the results derived from analytical techniques. Averaging Averaging is not always appropriate and its use may destroy or disguise the original signal characteristics. This includes, for example, signals arising from intermittent defects or averaging of non-steady signals. It may be possible to use non-steady signal techniques to give a better understanding of the signal characteristics. Root mean square (r.m.s.) averaging will give a better estimate of the value of a signal, but it will not improve the signal-to-noise ratio. Linear averaging will improve the signal-to-noise ratio if a trigger signal is available which is synchronous with the periodic part of the signal. 3.1.6

Modulation Modulation describes a time dependant variation, either random or repetitive, in a vibration signal, Figure 3.2. •

• •

Amplitude modulation arises, for example, in an eccentrically mounted gear where the tooth meshing frequency is constant but the amplitude varies, typically at once per revolution of the gear. Frequency modulation occurs, for example, in gears with tooth spacing errors or the passing signal from torsionally vibrating gear teeth. Phase modulation occurs, for example, onboard a twin screw ship where the excitation varies in time.

These types of modulation can occur in the same signal, for example in heavy weather where the speed and load of a ship’s main engine may vary simultaneously or in the hunting of a governor of an alternator set. Frequency analysis cannot describe the varying amplitude and frequency. The information is interpreted as steady sine waves which appear as sidebands about the fundamental frequency. The amplitude of the fundamental frequency may be significantly diminished in cases of very heavy modulation. One side effect of modulation is that the ear may detect frequencies that do not exist or may be outside the normal range of audible frequencies. Figure 3.2 Vibration modulation

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Ship Vibration and Noise Guidance Notes

3.1.7

Section 3

Rolling element envelope analysis Incipient defects in rolling element bearings produce sharp pulses which may produce measurable frequencies up to 20 kHz. Identification of the source cannot be carried out using simple FFT analysis and a technique known as envelope analysis is used to extract useful information from the vibration signal as follows. First the time domain signal is band-pass filtered around the region of high frequency energy. This leaves a signal containing bursts of energy at the defect frequency, which is then rectified and low-passfiltered. An FFT analysis of the resultant signal will allow the defect frequency to be identified. Calculation of the impact rates is given in Figure 3.3.

3.1.8

Calibration Analysis methods should be verified using known input data. Any software used in calibration, measurement or analysis should be part of an appropriate Quality Assurance system. Figure 3.3 Calculation of rolling element impact frequencies. Contact angle, β Ball diameter, B

Pitch diam, P

Impact frequencies, f Hz, assuming pure rolling:

n ⎞ ⎛ B . f . ⎜1 - . cos β ⎟ 2 r ⎝ P ⎠ n ⎞ ⎛ B Inner race defect, f = . f r . ⎜1 + . cos β ⎟ 2 ⎠ ⎝ P

Outer race defect,

f=

2⎤ ⎡ P ⎞ ⎛B . f r . ⎢1 - ⎜ . cos β ⎟ ⎥ B ⎢ ⎝P ⎠ ⎥ ⎣ ⎦ n = number of balls or rollers

Ball / roller defect, f = where

f r = relative revolutions per second between inner and outer races B = ball or roller diameter P = race pitch diameter

β = contact angle

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SECTION 3

3.2

Analysis for ISO 6954:1984

3.2.1

This section details Lloyd’s Register’s interpretation of ISO 6954:1984 Mechanical Vibration and shock -Guidelines for the overall evaluation of vibration in Merchant Ships (1984). It should be used in conjunction with Section 6.5. The analysis is different to that used in ISO 6954:2000 and users should ensure that the appropriate version is being used.

3.2.2

Derivation of Vibration Levels In order to define the correct procedure for interpretation of FFT analysis, it is useful to consider how the guidance vibration levels of ISO 6954:1984 were originally derived. The measure of vibration severity used in ISO 6954:1984 is termed the maximum repetitive amplitude (MRA). The MRA is defined as the largest repeating value of the modulated signal of a single frequency obtained during sea trials. The sea trials are to be conducted in accordance with ISO 4867: Code for the measurement and reporting of shipboard vibration data and / or ISO 4868: Code for the measurement and reporting of local vibration data of ship structures and equipment. The usual measuring system employed to collect the vibration data used in formulating the original guidance limits of ISO 6954:1984 included a chart recorder that provided a paper trace of the vibration signal. This trace was then manually analysed to determine the MRA for each significant excitation source. A representation of a typical propeller excited hull vibration is shown in Figure 3.4. It indicates modulation of the vibration amplitude due to variation of the propeller excitation forces. This vibration signal has been filtered to show only propeller blade passing frequency from which the MRA is readily identified. The value indicated is the peak-to-peak value, or twice the MRA. This is the value to be compared with the guidance levels given is ISO 6954:1984. MRA’s for individual excitation frequencies can be readily evaluated using a sea trials measuring system that includes a chart recorder, a tape recorder and precision filters. However, this is laborious, and an FFT analyser is often used to provide a spectral analysis of the vibration signal. Unfortunately, as a consequence of the averaging process used in an FFT analyser, the modulation effects are suppressed and the MRA is obscured. A direct reading of the MRA as required by ISO 6954:1984 is not possible and it is therefore necessary to apply a correction factor in order to estimate the MRA. Figure 3.4 Maximum repetitive amplitude

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Ship Vibration and Noise Guidance Notes

3.2.3

Section 3

Use of FFT Analysers When using an FFT analyser to provide the frequency spectra of a vibration signal there are, on a typical analyser, three analysis methods available, namely: • • •

r.m.s. average peak average peak hold - not to be used for MRA estimates.

Each of these methods calculates a time-averaged level of vibration over the recorded signal length and, as a consequence of the averaging process, the true MRA cannot be directly calculated. Of these three averaging methods, the analysis procedure that most accurately reflects the true value of the MRA, as defined in ISO 6954:1984, is as follows: • •

Calculate the average r.m.s. value of vibration over the frequency range 1 - 100 Hz. The record should be at least two minutes long. Multiply the average r.m.s. spectral values by a crest factor of 2.5 for propeller excited vibration to allow direct comparison with typical chart recorder traces or the ISO 6954:1984 guidelines.

The crest factor of 2.5 comprises: • •

A factor of 1.414 to convert from r.m.s. to peak values. A tentative conversion factor of 1.8, as proposed in ISO 6954:1984, to account for the normal modulation of the vibration signal in sea state 3. The conversion factor is defined as the ratio of MRA to the average amplitude during steady speed trials.

It is stressed that the conversion factor of 1.8 is a tentative value that may vary between ships and/or trial conditions. It is therefore essential that the measuring equipment employed during sea trials provide a recording of the time based vibration signal, either digitally or on magnetic tape, so that if required, the true conversion factor can be calculated. This may be necessary in the event of possible design problems or questions relating to compliance with design specifications. For example, structural vibration due to machinery excitation is unlikely to have the degree of modulation typically associated with propeller excitation and therefore the use of 1.8 as the conversion factor will lead to an over estimate of the MRA. 3.2.4

Recommended analysis procedure In the examination or the interpretation process of vibration signals, the fundamental step is to identify the excitation sources. For vibrations due to machinery, a factor of 1.414 to convert from r.m.s. values to peak values is normally adequate to assess the vibration severity. For propeller induced vibrations, however, a more cautious approach will be adopted. In the case where the vibrations caused by propeller excitation are not considered to cause any complaints and that the levels are well within design specifications, the use of a crest factor of 2.5 is acceptable. However, in the event that the vibration levels are marginally within the design specifications and that possible problems or argument may arise, the vibration signals will then be subjected to vigorous examination in order to establish the true conversion factor. This examination process is:

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Ship Vibration and Noise Guidance Notes

SECTION 3

• •

• •

to play back the recorded signal from a tape recorder onto an oscillograph measuring device to obtain a paper trace of the vibration signal; a ‘filter’ will be used during the above play back process so that only the vibration signals related to the propeller blade passing frequency will be examined. The filter response and the bandwidth should be wide enough to capture the quickest modulations; the recorded signal on the paper trace should be long enough to allow the establishment of MRA and the average amplitude; the true crest factor will then be calculated from the MRA and average amplitude.

3.3

Analysis for ISO 6954:2000

3.3.1

This section details Lloyd’s Register’s interpretation of ISO 6954:2000 Mechanical Vibration and Shock – Guidelines for the overall evaluation of vibration in Merchant Ships (2000). It should be used in conjunction with Section 6.6. The analysis is different to that used in ISO 6954: 1984 and users should ensure that the appropriate version is being used.

3.3.2

The vibration level is defined as an overall frequency weighted r.m.s. velocity for all vibrations within a range of 1 to 80 Hz. Acceleration may also be used. The weighting functions, from ISO6954:2000 are reproduced in Table 3.1 and Figure 3.5. The weighting functions are applicable to all directions. Table 3.1 Weighting functions for ISO 6954:2000.

18

Band

Velocity

Acceleration

Band

Velocity

Acceleration

Hz

Wv

Wa

Hz

Wv

Wa

0.20

0.002

0.063

10.00

0.869

0.494

0.25

0.004

0.099

12.50

0.911

0.412

0.32

0.009

0.156

16.00

0.941

0.337

0.40

0.017

0.243

20.00

0.961

0.274

0.50

0.032

0.369

25.00

0.974

0.220

0.63

0.059

0.530

31.50

0.979

0.176

0.80

0.098

0.701

40.00

0.977

0.140

1.00

0.147

0.833

50.00

0.964

0.112

1.25

0.201

0.907

63.00

0.926

0.083

1.60

0.261

0.934

80.00

0.843

0.060

2.00

0.327

0.932

100.00

0.706

0.040

2.50

0.402

0.910

125.00

0.533

0.024

3.15

0.485

0.872

160.00

0.370

0.013

4.00

0.573

0.818

200.00

0.244

0.007

5.00

0.661

0.750

250.00

0.156

0.004

6.30

0.743

0.669

315.00

0.100

0.002

8.00

0.813

0.582

400.00

0.063

0.001

Lloyd’s Register

Ship Vibration and Noise Guidance Notes

Section 3

Figure 3.5 Weighting functions for ISO 6954:2000. 10

Velocity weighting, Wv

Frequency weighting

1

0.1

Acceleration weighting, Wa

0.01

0.001 0.1

1

10

100

1000

Frequency (Hz)

3.3.3

Record length Analysis of recorded measurements should be made for a period of at least one minute, or two minutes if there are dominant components below 2 Hz. For unsteady vibrations with significant modulation, such as structural response to propeller induced vibration forces, it may be necessary to extend further the measurement and the corresponding analysis periods in order to derive reliable values of overall r.m.s. vibration velocity.

3.3.4

Analysis options Analysis of the measured data may be undertaken in either the time or frequency domains. The availability of portable FFT signal analysers means that a frequency domain analysis will be preferred by most vibration engineers. The procedure consists of three steps: • • •

3.3.5

spectral analysis (constant or proportional bandwith), followed by signal weighting, and finally summation of weighted spectral components.

FFT analyser settings Typical FFT parameters for a 400-line analyser are: • • • • • •

Lloyd’s Register

Hanning window Frequency range, 0-100 Hz (nearest to 1-80 Hz) Sampling frequency, 250Hz Number of data in each sample: 1024 Sample length: 4.096 seconds Averaging r.m.s. over 15 samples, no overlap.

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Ship Vibration and Noise Guidance Notes

SECTION 3

3.3.6

Calculation of overall weighted value The overall weighted value is determined from:

aw

⎡ 2 ⎤ = ⎢∑ a wi ⎥ ⎣ i ⎦

1/ 2

Where: aw = frequency-weighted acceleration or velocity. awi = weighted acceleration or velocity for the i th one-third octave band 3.3.7

Direction The highest value in any direction will be used for assessment.

3.4

Noise

3.4.1

Noise Rating Curves

3.4.2

Noise Rating (NR) curves are used in the IMO Code on Noise Levels on board Ships and in statutory codes and were incorporated into ISO 1996. They are a set of empirical curves relating the linear octave band pressure level to the centre frequency of the octave bands each of which is characterised by a Noise Rating number which is numerically equal to the sound pressure level given by the curve at 1000 Hz, Figure 3.6. The subjective effect of the noise is predicted from the NR number. The octave band sound pressure levels are plotted on the NR curves. The NR number is that NR curve to which the highest plotted octave level is anywhere tangent.

3.4.3

Narrowband analysis of noise The narrowband analysis of noise is useful in locating sources which are dependant upon speed of rotation and give rise to pure tones, for example, fans at blade passing frequency.

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Ship Vibration and Noise Guidance Notes

Section 3

Figure 3.6 Noise rating curves

140

130

130

125 120

120

115 110

110

Octave band pressure level, dB re 20 micro Pascal

105 100

100

95 90

90

85 80

80

75 70

70

65 60

60

55 50

50

45 40

40

35 30

30

25 20 31.5

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20 63

125

250 500 1000 2000 Octave band centre frequency, Hz

4000

8000

21

SECTION 3

Ship Vibration and Noise Guidance Notes

3.5

Hull surface pressure data

3.5.1

Cavitation induced signatures can take the form of either discrete harmonics (blade orders) or have a broadband character. The signals are also non-steady and, therefore, the measurement needs to take account of this. The non-steady character may be a function of any propeller blade to blade geometry differences, temporal and spatial wake fluctuations, and water quality and environmental changes.

3.5.2

Time series data are most commonly reduced to their constituent frequency content using Fast Fourier Transform (FFT) analysis techniques. Such processes generate frequency spectra of pressure amplitudes and phases averaged over the length of the time series records which contain several hundred blade passages. Such a procedure does not distinguish the contributions made by individual blades or account for discrete bursts of activity.

3.5.3

To establish the nature of the pressure signal time histories, in particular beating type effects, the measurements should be viewed as time series to present the relationship between pressure and propeller angular position. The pressure signatures should be considered over both short and long time frames.

3.5.4

To distinguish short time frame events alternative methods of analysis are necessary. Such methods would include Joint Time Frequency Analysis (JTFA) in which segments of the signal are analysed individually and the frequency content is obtained as a function of time. Such procedures can be extended to the separate analysis of the signatures from each blade.

3.5.5

When available, synchronised high-speed video and pressure signals should be presented to assist in connecting cavity and pressure events to identify the source of the higher harmonic content of the signals.

3.5.6

Pressure spectra and 1/3rd octave band analysis should be presented in order to supplement the amplitudes extracted at multiples of the blade passing frequency.

3.5.7

Hull pressures should be given as single amplitude peak values (half the peak-to-peak).

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Ship Vibration and Noise Guidance Notes

Section 4.

Section 4

Ship structure vibration

4.1

Hull girder

4.1.1

Resonance A ship’s hull will respond to exciting forces and moments as a beam freely supported in water. The modes are described by the plane of vibration and the number of nodes (points of no deflection); for example, the two-node vertical, Figure 4.1. Frequencies are low, typically in the range 1-10 Hz. The excitation may come from engine external forces or moments, propeller pressure impulses or, irregularly, by waves. Wave excitation frequencies are typically 1-2 Hz.

Figure 4.1 Hull girder modes of vibration.

2-node vertical or horizontal

3-node vertical or horizontal

Torsional

At resonance, when excitation and hull girder natural frequencies coincide, dynamic magnification may result in large amplitudes of vibration for comparatively low excitation. Hull girder natural frequencies are dependant on the stiffness and mass of the structure and the virtual added mass of water. They vary with changes in draught, trim, and mass distribution. Resonances above the normal operating speed of the vessel in ballast may move down the speed range and become troublesome in the loaded condition. Investigation of hull girder vibration is fundamental to identification of the possible causes of high shipboard vibration. 4.1.2

Measurement positions It is normal to measure hull girder response at the stern or, alternatively, at the sterntube, Figure 4.2. Measurements at the sides will allow torsional hull modes to be identified and simultaneous measurements at the wheelhouse and the main engine (if a slow speed diesel) will provide additional information about superstructure and engine modes.

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Ship Vibration and Noise Guidance Notes

SECTION 4

Figure 4.2 Measurement positions.

Bridge Stern

Sterntube

4.1.3

Main engine

Avoidance of resonance in service Resonances of the ship’s structure are normally lightly damped and finely tuned so that an adjustment of the shaft speed by a few revolutions either way may reduce the response. It may be possible to alter the frequency or magnitude of the excitation source, for example, changing the number of blades on a propeller or changing to a highly skewed or tipunloaded propeller blade form. It is generally not practical to change the natural frequencies of hull girder modes by altering the steelwork or to reduce the response by additional damping.

4.1.4

Avoidance of resonance by design 3-D finite element analysis can be used at the design stage to model a ship’s structure. Reliable estimates can be made of natural frequencies which might be excited at service speed. Campbell diagrams are a useful tool here in plotting excitation and response frequencies.

4.1.5

Forced vibration Forced vibration may occur when propeller pressure impulses or engine external forces and couples are large. Amplitudes increase with transmitted shaft torque and are generally proportional to the square of the speed with a fixed pitch propeller. A reduction in the excitation level is usually necessary if forced vibration levels are excessive.

4.2

Superstructure modes Superstructure vibration may be caused by vibration of the hull girder or resonant behaviour of the deckhouse, Figure 4.3. A lack of deckhouse stiffness and poor vertical support or continuity will exacerbate vibration levels.

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Ship Vibration and Noise Guidance Notes

Section 4

Figure 4.3 Ship superstructure modes of vibration. Shear deflection

Rigid body - elastic support

Rigid body - hull girder deflection

4.3

Acceptable vibration levels Excessive vibration of the ship’s structure manifests itself as cracking of the ship’s structure (e.g. bulkheads, tanks), failure of equipment (e.g. radars), and uncomfortable living and working conditions. Guidance values for these as local phenomena are given elsewhere in these Guidance Notes.

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25

Ship Vibration and Noise Guidance Notes

SECTION 5

Section 5. 5.1

Local structural vibration

General Guidance values are based on Lloyd’s Register’s full scale experience of vibration induced structural cracking. The principal source of the data concerns the vibration of panels relative to their stiffened boundaries. Structural fatigue is a complex failure mode and of necessity the guidance values have a broad stippled zone to cater for the wide variations encountered with regard to: • • • • •

structural configurations and geometry vibration mode weld details workmanship environment.

It should be noted that the natural frequencies of tank panels are significantly influenced by the density and level of liquids within the tank. Damage may therefore only occur during particular cargo or operating conditions. 5.2

Scope The assessment criteria are restricted to locally magnified vibrations of steel structural elements relative to the boundaries with regard to the risk of cracking. The frequency range considered is 5 to 100 Hz.

5.3

Assessment The assessment levels are shown in Figure 5.1 and apply to unidirectional narrowband measurements taken at the position of maximum vibration amplitude such as at the centre of panels or tank sides. It is recommended that the overall vibration amplitudes (peak) for vibrations in the frequency range 5 to 100 Hz are less than each of the following values: • • •

5.4

displacement ± 0.25 mm peak velocity ± 30 mm/s peak acceleration ± 20 m/s2 peak.

Alternative techniques Structural vibrations may be assessed by dynamic strain measurements in conjunction with other relevant data to define the fatigue environment. Modal and finite element analyses may give a better understanding of the behaviour of structures. The assumptions implicit in such analyses should be validated by measurements.

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Ship Vibration and Noise Guidance Notes

Section 5

1

10

m m

m m

Figure 5.1 Local structural vibration.

0 10

Damage probable

/s² m Di sp la ce m en t, ±

Velocity (peak), ± mm/s

m m

0. 1

m m

100 mm/s

,± ion at ler ce Ac /s² m

10 /s² m

Recommended

0. 01

m m

10 mm/s

1 ² /s m

1 mm/s 100

² /s m

/s² m

Lloyd’s Register

10 Frequency, Hz

1 0.

01 0.

1

27

Ship Vibration and Noise Guidance Notes

SECTION 6

Section 6.

Accommodation and workspace vibration

6.1

Scope

6.1.1

The scope of this section is the evaluation of hull and superstructure vibration with regard to crew habitability in all normally occupied spaces. The vibration levels given in this section do not apply to passenger cabins or other passenger spaces except in so far as they are working areas.

6.1.2

The evaluation applies to normal service operating conditions with the main propulsion machinery developing at least 85% of the maximum continuous rated power. The evaluation is not intended to apply to manoeuvring conditions or operation in heavy weather.

6.2

Measurements

6.2.1

Measurements should be taken on the deck in three mutually orthogonal directions: vertical, athwartships and longitudinal.

6.2.2

Where normal transducer attachment methods are impractical, due to the presence of deck coverings such as carpets, an inertia block with a mass of at least 1kg with spiked supporting legs may be used to locate the transducers.

6.2.3

In cabins, vibration readings are to be taken in the centre of the floor area. For larger spaces, such as mess rooms and the navigating bridge, sufficient measurements should be taken to define the vibration characteristics.

6.3

Test conditions

6.3.1

Measurements should be taken with the vessel proceeding ahead at a constant speed and straight course in a depth of water not less than five times the draught.

6.3.2

Tests should be conducted in sea conditions not greater than sea state 3 (slight).

6.3.3

The vessel should be at a displacement and trim corresponding to a normal operating condition.

6.3.4

Rudder angle variations should be limited to ± 2° of the amidships position.

6.4

ISO 6954:1984 and ISO 6965:2000

6.4.1

ISO 6954:1984 Guidelines for the overall evaluation of vibration in merchant ships have been superseded by ISO 6954:2000. At the time of writing (2006) the latter version remains to be widely adopted. This reflects the considerable experience which exists among shipowners, shipbuilders, operators and Classification Societies with regard to the application and interpretation of the earlier version. This suggests that ISO 6954:1984 will remain in general use as a specification requirement until confidence has been established in ISO 6954:2000.

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Ship Vibration and Noise Guidance Notes

Section 6

6.4.2

Assessment criteria and limits for both standards are given below. The measurement parameters, frequency range, analysis methods, and severity criteria are different for the two versions and care must be taken to define which one is being used.

6.5

Lloyd’s Register’s assessment of accommodation and workspaces based on ISO 6954:1984

6.5.1

The guidance values are based on ISO 6954:1984 Mechanical Vibration and shock -Guidelines for the overall evaluation of vibration in Merchant Ships (1984). The limits of this Standard have been adopted as Figure 6.1 of the Guidance Notes. The amendments and interpretation are intended to facilitate: simpler analysis of routine survey measurements; evaluation of the sum of two or more frequency components; and differentiate between rest and working areas.

6.5.2

The severity criteria are intended to apply to the position of maximum vibration within the space under consideration. Vibrations in each of the three orthogonal directions should be assessed independently. Analysis of measurements should be in accordance with Section 3.2.

6.5.3

Broadband measurements. The following severity classification applies to broadband measurements of the maximum overall vibration amplitude (peak) for vibrations within the frequency range 1 to 100 Hz. The values are the maximum repetitive amplitudes which occur during a minimum measuring period of 60 seconds. Vibration levels are normal if: • Velocity is below ± 6 mm/s peak,

or •

Acceleration is below ± 0.15 m/s2 peak.

Vibration levels are excessive if: • Velocity exceeds ± 15 mm/s peak,

and •

Acceleration exceeds ± 0.30 m/s2 peak.

For intermediate vibration levels severity should be assessed from a narrowband frequency analysis as described in Paragraph 6.5.3. 6.5.4

Narrowband measurements. Broadband measurements of vibration having levels which fall between the normal and excessive levels given in Paragraph 6.5.2 should be assessed using a narrowband frequency analysis in relation to the guidance values shown in Figure 6.1. Values are the maximum amplitudes of individual narrowband components which occur during a minimum measuring period of 60 seconds. No single component should exceed the “upper boundary”. For sleeping and rest areas only one component may be within the stippled zone.

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Ship Vibration and Noise Guidance Notes

SECTION 6

1

10

m m

m m

Figure 6.1 Accommodation and workplace vibration levels.

0 10 /s² m Di sp la ce m en t, ±

Velocity (peak), ± mm/s

m m

0. 1

m m

100 mm/s

,± ion at ler ce Ac

Adverse comments probable

/s² m

10 /s² m 0. 01

m m

10 mm/s

Adverse comments not probable 1 ² /s m

1 mm/s 100

² /s m

/s² m

30

10 Frequency, Hz

1 0.

01 0.

1

Lloyd’s Register

Ship Vibration and Noise Guidance Notes

Section 6

6.6

Assessment accommodation and workspaces based on ISO 6954:2000

6.6.1

Guidance values are based on ISO 6954:2000 Guidelines for the overall evaluation of vibration in merchant ships.

6.6.2

The severity criteria are intended to apply to the position of maximum vibration within the space under consideration. Vibrations in each of the three orthogonal directions should be assessed independently. Analysis of measurements should be in accordance with Section 3.3.

6.6.3

The recommended maximum acceptable values of frequency weighted r.m.s. vibration velocity are given in Table 6.1. for vibration within the frequency range 1 to 80 Hz. Table 6.1 Accommodation and workplace vibration levels. Normal

Excessive

Frequency weighted r.m.s. mm/s. Crew accommodation areas Working areas

4.5

6

6

8

6.7

Other ship types, PCAC

6.7.1

Vibration habitability criteria for passenger ships, high speed craft and yachts are given in LR’s Provisional Rules for Passenger and Crew Accommodation Comfort, (PCAC).

6.7.2

These Rules define the vibration severities in all relevant areas of the vessel for classifications of passenger comfort. Additionally, criteria are given for crew accommodation and working spaces which can be applied to conventional merchant ships where an enhanced comfort standard is required in relation to the basic acceptability limits given above in Sections 6.4, 6.5 and 6.6.

6.7.3

The PCAC Rules also stipulate more comprehensive test conditions and survey procedures that must be followed if a Class comfort notation is assigned to the vessel.

6.8

Motion sickness Motion sickness is influenced by a number of factors such as translational and rotational oscillations, constant speed rotations about an off-vertical axis, Coriolis stimulation and movements of the visual scene. Whilst some types of motion can be reliably predicted to result in more nausea than others, motion sickness is neither explained nor predicted by dynamics. Biological factors such as age and sex also have an influence. Acceleration, exposure time, and frequency of motion can be used to derive motion sickness indices, such as the Motion Sickness Dose Value (MSDV) described in ISO 2631. Motion sickness may be expected to occur in some unacclimatized people at accelerations greater than 2 to 3 m/s2 at roll periods of around 10 seconds for normal ship type hulls.

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Ship Vibration and Noise Guidance Notes

SECTION 7

Section 7.

Machinery vibration

7.1

Introduction.

7.1.1

Measurements should be taken with the machine operating at normal temperatures.

7.1.2

The assessment criteria apply to all operating speeds and loads for which the running conditions are stable.

7.1.3

With the exception of main propulsion machinery, broadband measurements may be used for assessment if the vibration severity with the machinery operating is greater than three times the background value with the machine stopped. Otherwise narrowband analysis is required.

7.1.4

Narrowband severity should be assessed on the amplitudes of the frequency components generated by the machine itself.

7.2

Rotating machines

7.2.1

Assessment criteria The assessment criteria are given in Table 7.1. Table 7.1 Rotating machinery assessment 50.0 Excessive

Overall vibration velocity, mm/sec r.m.s.

20.0

Excessive

18.0

11.2

Unsatisfactory

Excessive 10.0 Excessive

7.1

Unsatisfactory

7.1

4.5

Unsatisfactory

4.5

Satisfactory

Unsatisfactory

2.8

Satisfactory

2.8

1.8

Satisfactory

1.8

Good

Satisfactory

1.12

Good

0.71

Good

1.0

Good Small machines 40

0.64 2)

0.8 2)

40 2)

50 2)

25 2)

31 2)

≥ 2000

≤ 40

0.8

0.95

50

60

31

38

< 2000

> 200

0.72

0.32

0.45

45

20

28

28

13

18

≥ 1300

≤ 200 > 100

0.72

0.4

0.48

45

25

30

28

16

19

≤ 100 > 40

0.4

0.48

25

30

16

19

> 1000

0.29

0.35

18

22

11

14

< 1300 > 720

≤ 720

≤ 1000 > 200

0.72

0.32

0.39

45

20

24

28

13

15

> 1000

0.72

0.24

0.32

45

15

20

28

9.5

13

Notes: 1) Equivalent electrical power, kVA = cos ϕ .kW where cos ϕ = 0.8 (typically). 2) These values are subject to agreement between the manufacturer and customer. 3) Where generators are coupled to the flange housing of the engine the values measured at the engine end of the generator shall meet the values for generators.

7.6

Reciprocating compressors The values given in Figure 7.2 for reciprocating machinery are applicable.

7.7

Main propulsion gearboxes Main propulsion gearboxes should be assessed as rotating machinery using Table 7.1.

7.8

Rolling element bearings Rolling element vibration measurements may require special instrumentation because the defect frequencies may be above the frequency response range of general purpose vibration instruments. Various parameters have been developed such as shock pulse, spike energy, curtosis factor, and acceleration crest factor. The measured values are dependent on the instrumentation used and there are no internationally accepted standards. The most useful technique for fault finding is considered to be the envelope analysis described in Section 3.1.7. Otherwise, the recommended procedure is to make regular, periodic measurements and observe the trend of the levels.

7.9

Pipework Pipe vibrations can be assessed in the first instance using Figure 7.3. The guidance values are based on experience ashore in the petrochemical industry.

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Ship Vibration and Noise Guidance Notes

SECTION 7

Figure 7.3 Pipeline vibration.

2.00

1.00

Vibration displacement, ± mm

Da

nge r

Co rr e ct i o n Ma 0.10

rg i n al

De s ig n

Pe r ce pti

on

0.01

0.005 1

38

10 Frequency, Hz

100

Lloyd’s Register

Ship Vibration and Noise Guidance Notes

7.10

Section 7

Electrical control and instrumentation IEC 92-504 requires that electrical, electronic and programmable equipment intended for control, monitoring, alarm, and protection systems in ships should operate satisfactorily within the following conditions: General shipboard conditions. • displacement amplitude ± 1.5 mm in the frequency range 2 Hz - 13 Hz. • acceleration amplitude ± 10 m/s2 in the frequency range 13 Hz -100 Hz. At special locations, for example directly on all engines, diesel engine exhaust systems, diesel generator sets, compressors, and in steering gear rooms: • displacement amplitude ± 1.5 mm in the frequency range 2 Hz - 28 Hz. • acceleration amplitude ± 50 m/s2 in the frequency range 28 Hz -100 Hz.

7.11

Vortex shedding Vortex shedding from the alternate downstream sides of a bluff body in a fluid flow may excite structural resonances, for example, in boiler economiser tubes, chimneys, fins, or propeller blades. The frequency of shedding is given in terms of the Strouhal number, Sn, and this in turn is a function of the Reynolds number, Re. The Strouhal number is defined as: f =

S n ⋅ V0 d

where: f

= frequency of shedding of vortices, Hz.

Sn = Strouhal number ≈ 0.2 very approximately for rough surfaces and Re in the range 3 x 102 to 3 x 105. V0 = free-stream velocity, m/s. d = Re =

effective diameter of trailing edge or characteristic width, m. V0 ⋅ d

υ

υ = kinematic viscosity of fluid (dynamic viscosity/density), m2/s.

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39

Ship Vibration and Noise Guidance Notes

SECTION 8

Section 8. 8.1

Noise

Scope This section applies to ships in service, in port or at sea with a crew on board, including passenger ships.

8.2

Objectives The maximum noise levels in the Guidance Notes are given to: • protect seafarers from noise levels which may give rise to noise-induced hearing loss • provide an acceptable degree of comfort in rest, recreation and other spaces • provide conditions for recuperation from the effects of exposure to high noise levels • provide safer work places by facilitating speech communication and hearing of alarms in control stations, navigation and radio spaces, and manned machinery spaces.

8.3

Test conditions Conditions during the measurements should conform to Table 8.1. The actual conditions should be noted, as well as the ship’s draughts, course, depth of water, equipment used, and name of observer and organization.

8.4

Measuring positions Measurements should be made at the positions given in Table 8.2.

8.5

Assessment

8.5.1

The maximum acceptable sound pressure levels should not exceed the values given in Table 8.3 which are identical to those given in IMO Code on noise levels on board ships.

8.5.2

The levels given in Table 8.3 do not apply to passenger cabins or other passenger spaces except in so far as they are workplaces.

8.5.3

Where the recommended maximum level in Table 8.3 is exceeded by 3 dBA, or contains subjectively annoying low frequency or obvious tonal components, the noise levels in the octave bands centred on 31.5 to 8000 Hz (linear, without A-weighting) should be measured to determine the noise rating (NR) number in accordance with ISO 1996. The limits are satisfied if the Noise Rating is no higher than the dBA limit minus five. Noise rating curves are included in Figure 3.6.

8.6

Equivalent continuous sound level, LAeq An alternative to compliance with the limits given in Table 8.3 is to ensure that no seafarer without ear protection is exposed to a LAeq of more than 80 dBA. Daily exposure in spaces requiring the use of ear defenders (noise levels > 85 dBA) should not exceed 4 hours continuously or 8 hours in total.

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Ship Vibration and Noise Guidance Notes

Section 8

8.7

Other ship types, PCAC

8.7.1

Noise habitability criteria for passenger ships, high speed craft and yachts are given in LR’s Provisional Rules for Passenger and Crew Accommodation Comfort, (PCAC).

8.7.2

These Rules define the permissible noise levels in all relevant areas of the vessel for classifications of passenger comfort. Additionally, criteria are given for crew accommodation and working spaces which can be applied to conventional merchant ships where an enhanced comfort standard is required in relation to the basic acceptability limits given above in Section 8.5.1 and Table 8.3.

8.7.3

The PCAC Rules also stipulate more comprehensive test conditions and survey procedures that must be followed if a Class comfort notation is assigned to the vessel.

8.8

Noise transmission between cabins The airborne sound insulation properties for bulkheads and decks within the accommodation should comply with the weighted apparent sound reduction indices (R’w) according to ISO 717 given in Table 8.4.

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Ship Vibration and Noise Guidance Notes

SECTION 8

Table 8.1. Test conditions At sea: Draught:

Loaded or ballast.

Power:

Not less than 80% m.c.r.

Speed:

Normal service speed.

Ventilation:

Running at full capacity.

Equipment:

Auxiliary machinery to be operated normally.

Radio room:

Equipment in operation but without audible signals.

Wheelhouse

All equipment in operation, for example, radar, radio, window wipers. Weather side door and windows closed; lee side open and then closed

Bridge wings:

As far as practical with wind speed 5-10 knots and headings with wind ahead, astern and on both beams.

Ship’s whistle:

To be sounded for measurements at listening posts.

Emergency diesel, fire pump(s):

Measurements in the equipment spaces with it working. Not necessary in adjacent spaces with pump(s) operating unless equipment used for other than emergency and drills.

Weather

Wind force 4 (moderate breeze) and sea state 3 (slight) should not be exceeded.

In port: Engine room

Auxiliary machinery operating in “in port” condition.

Cargo gear:

Operating.

Car decks:

Measurements during loading and discharging.

Table 8.2. Measuring positions Accommodation General:

At least one measurement in every occupied space in the centre of the room with doors and windows closed. If noise level varies throughout space then extra readings at 7 m intervals including position of maximum noise should be taken.

Wheelhouse:

One extra reading at an open window.

Bridge wings:

At control positions on both wings when on leeside of wind.

Radio room:

In centre and at work position.

Galley/pantry:

With equipment not working and at 1m away from working equipment.

Ship’s whistle:

Measured at listening posts (bridge wings, forecastle).

Machinery spaces General:

1m from and at intervals not greater than 3 m around machinery.

Large engine rooms:

If readings at 3m intervals do not vary much, then four measurements on each level.

Spaces:

Machinery and cargo control rooms, workshops, stores, fan rooms, pump rooms, refrigerator rooms, steering gear room, access routes.

Machinery:

Engines at each level and local control stations, main gearing, turbo-blowers, purifiers, alternators, firing platforms, fans, compressors, cargo pumps. Machines under 5 kW may be excluded unless significant noise sources.

Unoccupied spaces Measurements are not required in normally unoccupied spaces, holds, or deck spaces which are remote from noise sources and a rough check shows that the noise levels are well below the limits.

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Ship Vibration and Noise Guidance Notes

Section 8

Table 8.3 Acceptable maximum noise levels for crew Working areas Radio room (equipment working, but no audio signals)

60 dBA

Wheelhouse, chartroom

65 dBA

Listening post, including bridge wings and windows

70 dBA

Recommended level in 250 Hz octave band

68 linear

Recommended level in 500 Hz octave band

63 linear

Galleys, pantries and serveries (equipment not working)

75 dBA

Machinery control rooms

75 dBA

Workshops

85 dBA

Normally unoccupied spaces, e.g. holds, decks

90 dBA

Machinery space, continuously manned, e.g. stores

90 dBA

Machinery space, not continuously manned, e.g. pump, refrigerator, thruster or fan rooms.

110 dBA

Accommodation Sleeping cabins, hospitals

60 dBA

Day cabins

65 dBA

Offices, conference rooms

65 dBA

Mess rooms, lounges, recreation areas within accommodation

65 dBA

Recreation areas on open deck

75 dBA

Alleyways, changing rooms, bathrooms, lockers

80 dBA

Ship’s whistle, at bridge wings or forecastle

110 dBA

Hearing protection Protection required when noise level exceeds

85 dBA

Overriding limits Maximum noise level, even when ear protection worn

120 dBA

Table 8.4 Weighted apparent sound reduction indices, R’w Crew accommodation Cabin to cabin

30 dB

Messrooms, recreation rooms to cabins and hospitals

45 dB

Table 9.1 RASTI Rating

Lloyd’s Register

RASTI Index

Intelligibility

0 - 0.3

Bad

0.3 - 0.45

Poor

0.45 - 0.6

Fair

0.6 - 0.75

Good

0.75 - 1.0

Excellent

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Ship Vibration and Noise Guidance Notes

SECTION 9

Section 9.

Audible alarms and public address systems

9.1

Audible alarm levels

9.1.1

Sound pressure levels due to audible alarms at the head position in bunks and at 1 m from the source should be at least 75 dBA and at least 10 dBA above ambient noise levels when the ship is sailing normally in moderate weather conditions. The sound pressure level due to an alarm should not exceed 120 dBA.

9.1.2

Audible alarms (with the exception of bells) should have a frequency in the range 2002500 Hz. The measured sound pressure level should be achieved in the third-octave band containing the fundamental frequency.

9.2

Public address system levels

9.2.1

The minimum sound pressure levels produced by speakers for broadcasting emergency announcements with the ship underway in moderate weather shall be: • 75 dBA and at least 20 dB above the speech interference level in interior spaces • 80 dBA and at least 15 dB above the speech interference level on open decks.

9.2.2

The minimum sound pressure levels due to the emergency alarm tone in interior spaces and on open deck with the ship underway in moderate weather should be 80 dBA and at least 10 dBA above ambient noise levels. At bunks and in bathrooms the levels should be the same as required for audible alarms in paragraph 9.1.1.

9.3

Speech intelligibility The transmission quality performance of a Public Address (PA) system with respect to speech intelligibility can be rated objectively by using the Rapid Speech Transmission Index (RASTI) method which is a simplified version of the Speech Transmission Index (STI)

9.3.1

Speech. Speech can be regarded as a flow of sound, with the spectrum varying continuously over time. Faithful speech transmission between any speaker-listener pair relies on preservation of these spectrum variations. For a PA system, speech transmission can be degraded by factors including the effects of the acoustic properties of the listeners’ enclosure such as reverberation and echoes, signal to noise level, equipment generated distortion and transmission bandwidth.

9.3.2

Modulation Transfer Function Signal degradation in an enclosure can be quantified by determining the Modulation Transfer Function (MTF) or M(F). The test signal is a noise carrier with a speech shaped spectrum, intensity modulated with a modulation frequency F. The MTF is the ratio of the modulation index mo of the signal at the listener’s position to the modulation index mi of the test signal.

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Ship Vibration and Noise Guidance Notes

9.3.3

Section 9

Speech Transmission Index The Speech Transmission Index (STI) is based on a set of measurements of the MTF for 7 octave bands from 125 Hz to 8 kHz and 14 modulation frequencies at third-octave interval from 0.63 Hz up to 12.5 Hz, giving 98 data points. The result is normalised to give a value between 0 and 1. The STI has been correlated with intelligibility scores obtained by subjective speaker-listener measurements.

9.3.4

Rapid Speech Transmission Index The RASTI method is restricted to two octave bands, centre frequencies 500 Hz and 2 kHz, and four or five modulation frequencies for the two octave bands, giving nine data points. This reduces the number of tests while covering a representative range of speech. The result is given as a value between 0 and 1.

9.3.5

RASTI Equipment and Measurement A signal from the RASTI Transmitter unit is input into the PA system, either electrically, or by positioning the unit on a tripod so that the external loudspeaker is located at the speaker’s position at the P.A. microphone. The RASTI receiver unit is placed at the test location, and the measurement carried out over 8, 16 or 32 seconds, with the signal broadcast over the PA system.

9.3.6

RASTI Rating The general relation between the quality of speech transmission with respect to intelligibility and the RASTI index is given in Table 9.1.

9.3.7

Sound Systems for Emergency Purposes. An STI of 0.5 or greater (measured using the RASTI technique) is required for sound systems for emergency purposes.

9.3.8

Diagnostics If the RASTI value is unsatisfactory, then the other measured parameters can be examined in order to identify the cause of the signal degradation, in particular the graph of the modulation reduction factors against the modulation frequency: • • •

9.4

A flat line is indicative of noise interference only. A negatively sloped line, indicative of reverberation interference only. A line with a sharp minimum can be indicative of a discrete echo or time delay.

Preferred Speech Interference Level The Preferred Speech Interference Level (SIL) is the arithmetic average of background noise in the 500, 1000, 2000 and 4000 Hz bands, measured in dB re 20 µPa.

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Ship Vibration and Noise Guidance Notes

SECTION 10

Section 10. Hull Surface Pressures 10.1

Introduction Hull surface pressures are generated by the action of the propeller operating in a nonuniform wake field. At normal tip clearances, the non-cavitating propeller tends to produce low hull pressures which have a dominant blade rate content. Cavitation occurs on most commercial propellers in the service speed/power range. Pressure signals typical of cavitating propellers show increased amplitudes at blade rate and distinct components at multiples of blade rate, typically up to 5 times blade rate. Two types of excitation are encountered: broadband and discrete harmonic. Susceptibility to troublesome levels of hull surface pressures depends on ship speed in association with thrust required, after body hull form, appendage design and clearances around the propeller. The effect of excitation from tip vortices on any unusual length of the afterbody of the ship beyond the propeller station needs careful consideration.

10.2

Hull surface pressure levels

10.2.1

Current practice suggests that a reasonable probability of achieving an acceptable vibratory behaviour for a ship due to hydrodynamic excitation can be obtained if the blade rate hull surface pressures given in Table 10.1 are not exceeded. The pressures are single amplitude peak values (half peak-to-peak). Table 10.1 Typical hull surface pressures Ship type

Typical blade rate hull surface pressure range ± kPa (peak)

Cruise ship

1-2

Ro/Ro Ferry

2-4

Container and fast cargo ships

3-6

Slow bulk carriers

4 -7

10.2.2

The higher blade rate harmonic hull pressures should always descend in a monotonic fashion with increasing harmonic number. As a guide, the magnitude of the twice blade rate component should be around half of the first, with the third being of very small proportions. Discrete harmonics beyond the third should be negligible.

10.2.3

Significant broadband excitation at up to 10 times blade rate frequencies should be avoided as these characteristics have the potential to excite a range of structural frequencies.

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Section 10

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Ship Vibration and Noise Guidance Notes

SECTION 11

Section 11. Related Standards, references and bibliography

11.1

Vibration - international standards

IEC 92-504 ISO 2041:1990

Electrical installations in ships. Special features: control and instrumentation.

ISO.2372

Mechanical vibration of machines with operating speeds from 10 to 100 rev/s - Basis for

Glossary of terms relating to mechanical vibration and shock specifying evaluation standards.

ISO.2373

Mechanical vibration of certain rotating electrical machinery with shaft heights between 80 and 400 mm - Measurement and evaluation of the vibration severity.

ISO.2631-1:1997

Mechanical vibration and shock - Evaluation of human exposure to whole-body vibration – Part 1: General requirements. Similar, but not identical to, BS.6841.

ISO.2631-2:1989

Mechanical vibration and shock - Evaluation of human exposure to whole-body vibration – Part 2: Continuous and shock induced-induced vibrations in buildings (1 to 80 Hz).

ISO.3945

Mechanical vibration of large rotating machines with speed range from 10 to 200 r/s Measurement and evaluation of vibration severity in situ.

ISO.4548-7:1990

Methods of test for full-flow lubricating oil filters for internal combustion engines - Part 7: Vibration fatigue test.

ISO.4866:1990

Mechanical vibration and shock - Vibration of buildings - Guidelines for the measurement of vibrations and evaluation of their effects on buildings.

ISO.4867:1984

Code for the measurement of and reporting of shipboard vibration data.

ISO.4868:1984

Code for the measurement of local vibration data of ships structures and equipment.

ISO.6954:1984

Mechanical vibration and shock - guidelines for the overall evaluation of vibration in merchant ships.

ISO 6954:2000

Mechanical vibration - Guidelines for the measurement, reporting and evaluation of vibration with regard to habitability on passenger and merchant ships

ISO.7919-1:1996

Mechanical vibration of non-reciprocating machines - Measurements on rotating shafts and evaluation criteria - Part 1: General guidelines.

ISO.7919-2:2001

Part 2: Land-based steam turbines and generator in excess of 50 MW with normal operating speeds of 1500rpm, 1800 rpm, 3000 rpm, and 3600 rpm.

ISO.7919-3:1996

Part 3: Coupled industrial machines.

ISO.7919-4:1996

Part 4: Gas turbine sets.

ISO.7919-5:1996

Part 5: Machine sets in hydraulic power generating and pumping plants.

ISO.8528-9:1995

Reciprocating internal combustion engine driven alternating current generating sets- Part 9:

ISO.8579-2

Acceptance code for gears - Part 2: Determination of mechanical vibrations of gears during

ISO.10816-1:1995

Mechanical vibration - Evaluation of machine vibration by measurements on non-rotating

ISO.10816-2:2001

Part 2: Land-based steam turbines and generator sets in excess of 50 MW with normal

ISO.10816-3:1998

Part 3: Industrial machines with nominal power above 15 kW and nominal speeds between

ISO.10816-4:1998

Part 4: Gas turbine sets excluding aircraft derivatives.

Measurement and evaluation of mechanical vibrations. acceptance testing. parts - Part 1: General guidelines. operating speeds of 1500rpm, 1800 rpm, 3000 rpm, and 3600 rpm. 120 rpm and 15000 rpm when measured in situ. ISO.10816-5:2000

Part 5: Machine sets in hydraulic power generating and pumping plants.

ISO.10816-6:1995

Mechanical vibration - Evaluation of machine vibration by measurements on non-rotating parts - Part 6: Reciprocating machines with power ratings above 100 kW.

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11.2

Section 11

Vibration – national standards

BS.3015:1991

Same as ISO 2041:1990

BS.5000:1980

Specification for Rotating machines of particular types or for particular applications. Part 3.

BS 6472:1992

Guide to evaluation of human exposure to vibration in buildings (1 Hz to 80 Hz)

BS.6632:1985

Same as ISO.4867

BS.6633:1985

Same as ISO.4868

Generators to be driven by reciprocating internal combustion engines.

BS.6634:1985

Same as ISO.6954

BS.6841:1987

Measurement and evaluation of human exposure to whole-body mechanical vibration and

BS.6842:1987

Measurement and evaluation of human exposure to vibration transmitted to the hand.

BS.7385:1990

Same as ISO.4866

BS.7698:1993

Same as ISO.8528

BS.7854

Same as ISO.10816

BS.ISO.7919

Same as ISO.7919

PD.12349:1997

Mechanical vibration - Guide to the health effects of vibration on the human body.

VDI 2063

Measurement and evaluation of mechanical vibrations of reciprocating piston engines and

repeated shock.

compressors. Report on the Survey of Marine Engine and Machinery Vibrations. Bulletin of the M.E.S.J. Vol 3 No. 3.

11.3

Noise – international standards

IEC 179:1973

Noise level meters.

IEC 225:1966

Octave, half-octave and third-octave band filters intended for the analysis of sounds and vibrations.

IEC 268-16 : 1988

Sound level meters, and Amendment 1:1993.

IEC 651:1979

Sound Systems for Emergency Purposes

IEC 804:1985

Integrating-averaging sound level meters, and Amendments 1:1989 and 2:1993.

IEC 942:1988

Sound level calibrators.

IEC 1260:1995

Electroacoustics – Octave-band and fractional-octave-band filters.

IEC 60268-16:1988

Sound system equipment. Guide to the 'RASTI' method for the objective rating of speech intelligibility in auditoria Code on Alarms and Indicators 1992

IMO Resolution

Code on noise levels on board ships.

A.468 (XII). 1982 ISO 266:1997

Acoustics -- Preferred frequencies.

ISO 717-1:1996

Acoustics – rating of sound insulation in buildings and of building elements. Part 1: Airborne sound insulation.

ISO 717-2:1996

Acoustics – rating of sound insulation in buildings and of building elements. Part 2: Impact sound insulation.

ISO 1996:-1:1982

Acoustics -- Description and measurement of environmental noise -- Part 1: Basic quantities and procedures

ISO 1996:-2:1987

Acoustics -- Description and measurement of environmental noise -- Part 2: Acquisition of data pertinent to land use

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Ship Vibration and Noise Guidance Notes

SECTION 11

ISO 1996:-3:1987

Acoustics -- Description and measurement of environmental noise -- Part 3: Application to noise limits

ISO 1999:1990

Acoustics -- Determination of occupational noise exposure and estimation of noiseinduced hearing impairment

ISO 2204:1979

Acoustics – Guide to international standards on the measurement of airborne acoustical noise and evaluation of its effects on human beings.

ISO 2922:2000

Acoustics -- Measurement of airborne sound emitted by vessels on inland waterways and harbours

ISO 2923:1996

Acoustics -- Measurement of noise on board vessels

ISO 8528-10:1998

Reciprocating internal combustion engine driven alternating current generating sets--

ISO 9921-1:1996

Ergonomic assessment of speech communication. Part 1. Speech interference level and

Part 10: Measurement of airborne noise by the enveloping surface method. communication distances for persons with normal hearing capacity in direct communication (SIL method).

11.4

Noise – national standards

BS 6840 : Pt 16 1989

Same as IEC 60268-16:1988

BS 7443:1991

Sound Systems for Emergency Purposes

BS ISO 9921-1:1996

Ergonomic assessment of speech communication.

BS.EN.22922:1993

Measurement of noise emitted from vessels on inland waterways and harbours.

D.o.T. (U.K.)

Code of Practice for noise levels in ships.

Danish Maritime

Technical Regulation No.5 of July 1997 on noise in ships.

Authority UKOOA

Guidance on Safety- Related Telecommunications Systems on Normally Manned Fixed Offshore Installations

11.5

References and bibliography

Hull pressure “Report of Propeller Committee”. Proceedings of the 16th. International Towing Tank Conference. USSR, 1981. Motion sickness Mandel, P. “Seagoing box scores and seakeeping criteria for monohull, SWATH, planing, hydrofoil, surface effect ships and air cushion vehicles”. David Taylor Research Centre (DTRC) Report SPD-79/1. 1979. Pipework Wachel, Morten and Atkins. “Piping vibration analysis.” Vortex shedding Wambsganss, M.W. “Understanding flow-induced vibrations”. Sound and Vibration, November 1976. Lloyd’s Register “Provisional Rules for Passenger and Crew Accommodation Comfort”.

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